public void textBox1_TextChanged(object sender, EventArgs e)
    {
        string ime=input_Ime.Text;
        var frm1 = new Form1();
        frm1.imee = ime;
    }

public string imee { get; set; }

public void button1_Click(object sender, EventArgs e)
    {
        MessageBox.Show(this.imee);
    }